Integrated Inventory Placement and Transportation Vehicle Selection using Neural Network

In this work, we investigate an integrated optimization problem of inventory placement and transportation vehicle selection in a logistics system with multiple central distribution centers and multiple regional distribution centers. The main decision in our problem refers to the selection of transportation vehicles, concerning the trade-offs among different types of costs in the system, such as the vehicle selection cost, commodity transportation cost and inventory holding cost. We formulate the problem as a nonconvex mixed-integer quadratically constrained program. Due to the nonconvexity of the objective function which makes the model difficult to solve, we establish a convex approximation on the proposed formulation using Cauthy inequalities. An efficient two-phase solution framework, combining neural network prediction and branch-and-bound search, is developed to solve the approximate model. Computational results demonstrate that using a neural network is effective in predicting values of a subset of integer variables in solution, which can be subsequently extended to form a high-quality solution to the integrated optimization. Moreover, the two-phase method has a significant advantage in solving speed over the pure implementation of branch-and-bound method, which suggests its strength in solving larger mixed-integer programs.